The ALEKS (Assessment and LEarning in Knowledge Spaces) educational software system is an instantiation of knowledge space theory (KST) that has been used by millions of students in mathematics, chemistry, statistics and accounting. The software employs a probabilistic assessment based on KST for placement into an appropriate course or curriculum, a learning mode in which students are guided through course material according to a knowledge structure, and regularly spaced re-assessments which are also based on KST. In each of these aspects, the interactions of the student with the system are guided by the theory and by insights learned from student data. We present several relationships between theory and data for the ALEKS system. We begin by surveying the ALEKS system and examining some practical aspects of implementing KST on a large scale. We then study the effectiveness of the ALEKS assessment using both standard statistical measures and ones adapted to the KST context. Finally, we examine the learning process in ALEKS via statistics for the learning mode and its associated knowledge structures.

ALEKS（知识空间中的评估和学习）教育软件系统是知识空间理论（KST）的实例，已被数百万学生用于数学，化学，统计学和会计。该软件采用基于KST的概率评估以放置到适当的课程或课程中，采用一种学习模式，在该学习模式中，根据知识结构对学生进行课程材料指导，并定期进行基于KST的重新评估。在这些方面的每一个方面，学生与系统的交互作用均以理论和从学生数据中学到的见解为指导。我们介绍了ALEKS系统的理论与数据之间的几种关系。我们首先调查ALEKS系统，并研究大规模实施KST的一些实际方面。然后，我们使用标准统计量度和适应KST情况的量度，研究ALEKS评估的有效性。最后，我们通过学习模式及其相关知识结构的统计数据检查ALEKS中的学习过程。